Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory

Abstract

We show an $\text{ab initio}$ construction of the energy density functional (EDF) for electron systems using the functional renormalization group. The correlation energies of the homogeneous electron gas given in our framework reproduce the exact behavior at high density and agree with the Monte-Carlo data in a wide range of densities. Our analytic technique enables us to get the correlation energies efficiently for various densities, which realizes the determination of EDF in the local density approximation (LDA) without any fitting for physically relevant densities. Applied to the Kohn-Sham calculation for the noble gas atoms, our EDF shows comparable results to those of other conventional ones in LDA.

arXiv comment6 pages, 4 figures, 1 table, v4: Fig. 3 and 4 modified, minor corrections in sentences, information of a reference updated

References in corpus (20)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• Functional renormalization group approach to correlated fermion systems
• The nonperturbative functional renormalization group and its applications
• Understanding and reducing errors in density functional calculations
• Introduction to the functional RG and applications to gauge theories
• Spin Polarization of the Low Density 3D Electron Gas
• Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas
• Density Functional Theory is Not Straying from the Path toward the Exact Functional
• Effective action and density functional theory
• Functional Renormalization Group and Kohn-Sham scheme in Density Functional Theory
• Towards a Renormalization Group Approach to Density Functional Theory - General Formalism and Case Studies -
• Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study
• Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem
• Comment on "Communication: Simple and accurate uniform electron gas correlation energy for the full range of densities" [J. Chem. Phys. 145, 021101 (2016)]
• Ab-initio description of excited states of a one-dimensional nuclear matter with the Hohenberg-Kohn-theorem-inspired functional-renormalization-group method
• Functional-renormalization-group aided density-functional analysis for the correlation energy of the two-dimensional homogeneous electron gas
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Generalized Kohn-Sham Density-Functional Theory via Effective Action Formalism

Cited by in corpus (10)

• Emergent Hadrons and Diquarks
• Toward ab initio charge symmetry breaking in nuclear energy density functionals
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• KIDS density functional for deformed nuclei: Examples of the even-even Nd isotopes
• Construction of energy density functional for arbitrary spin polarization using functional renormalization group
• Physics-informed neural networks for solving functional renormalization group on a lattice
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Relativistic correction of the Coulomb interaction in the local density approximation for energies and radii in doubly-magic nuclei
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems